Introducing the Huber mechanism for differentially private low-rank matrix completion

TL;DR

This paper introduces a novel Huber-based noise mechanism for differentially private low-rank matrix completion, demonstrating comparable or improved privacy-utility trade-offs over existing methods.

Contribution

The paper proposes a new Huber mechanism for differential privacy in matrix completion, combining robust statistics with privacy guarantees and empirical evaluation.

Findings

The Huber mechanism achieves epsilon-differential privacy similar to Laplace.

It outperforms Laplacian and Gaussian mechanisms in some scenarios.

The method is effective on both synthetic and real datasets.

Abstract

Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired by Huber loss, a well-known loss function in robust statistics. The proposed Huber mechanism is evaluated against existing differential privacy mechanisms while solving the matrix completion problem using the Alternating Least Squares approach. We also propose using the Iteratively Re-Weighted Least Squares algorithm to complete low-rank matrices and study the performance of different noise mechanisms in both synthetic and real datasets. We prove that the proposed mechanism achieves {\epsilon}-differential privacy similar to the Laplace mechanism. Furthermore, empirical results indicate that the Huber mechanism outperforms Laplacian and Gaussian in some cases and is comparable, otherwise.